Euclidean distance geometry : an introduction

Description

This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life. Front Matter ....Pages i-xiii Motivation (Leo Liberti, Carlile Lavor)....Pages 1-8 The Distance Geometry Problem (Leo Liberti, Carlile Lavor)....Pages 9-18 Realizing complete graphs (Leo Liberti, Carlile Lavor)....Pages 19-30 Discretizability (Leo Liberti, Carlile Lavor)....Pages 31-42 Molecular distance geometry problems (Leo Liberti, Carlile Lavor)....Pages 43-55 Vertex orders (Leo Liberti, Carlile Lavor)....Pages 57-65 Flexibility and rigidity (Leo Liberti, Carlile Lavor)....Pages 67-79 Approximate realizations (Leo Liberti, Carlile Lavor)....Pages 81-92 Taking DG further (Leo Liberti, Carlile Lavor)....Pages 93-96 Back Matter ....Pages 97-133